Question

find four rational number between I/2 and 5/7​

Answer 1

Answer:

ration number between 1/2 and 5/7

1/3

1/4

1/5

1/6

hope it helps you ( ◜‿◝ )

Answer 2

Step-by-step explanation:

Given:-

The two numbers are I/2 and 5/7

To find:-

Find four rational number between I/2 and 5/7?

Solution:-

Method-1:-

Given two numbers = I/2 and 5/7

1/2 can be written as

=>1/2 = (1/2)×(7/7)

=> 1/2 = 7/14

and

5/7 can be written as

=>5/7=(5/7)×(2/2)

=>5/7=10/14

Required rational numbers = 4

On writing the denominator as (4+1)=5 multiple

(7/14)×(5/5)

=> (7×5)/(14×5)

=>35/70

and

(10/14)×(5/5)

=>(10×5)/(14×5)

=>50/70

Now the rational numbers between 35/70 and 50/70 are 36/70,37/70,38/70,39/70,40/70,...,49/70

Method-2:-

Mean Method:-

The rational number between a and b = (a+b)/2

First rational number between 1/2 and 5/7

=>[(1/2)+(5/7)]/2

=>[ (7+10)/14]/2

=>(17/14)/2

=>17/28

The second rational number between 1/2 and 17/28

=> [(1/2)+(17/28)]/2

=> [(14+17)/28]/2

=> (31/28)/2

=> 31/56

The third rational number between 1/2 and 31/56

=> [(1/2)+(31/56)]/2

=> [(28+31)/56]/2

=> (59/56)/2

=>59/112

The fourth rational number between 1/2 and 59/112

=>[(1/2)+(59/112)]/2

=>[(56+59)/112]/2

=>(115/112)/2

=>115/224

The four rational numbers are 17/28,31/56,59/112,115/224

Answer:-

The rational numbers between 35/70 and 50/70 are 36/70,37/70,38/70,39/70,40/70,...,49/70

The four rational numbers are 17/28,31/56,59/112,115/224

Used formula:-

Mean Method:-

The rational number between a and b = (a+b)/2

Dense Property:-

There are infinitely number of many rational numbers between the two given numbers.